Bottom Line:
The technique of Quantitative Structure Property Relationships has been applied to the glass transition temperatures of polyarylethersulphones.A general equation is reported that calculates the glass transition temperatures with acceptable accuracy (correlation coefficients of between 90-67%, indicating an error of 10-30% with regard to experimentally determined values) for a series of 42 reported polyarylethersulphones.This method is quite simple in assumption and relies on a relatively small number of parameters associated with the structural unit of the polymer: the number of rotatable bonds, the dipole moment, the heat of formation, the HOMO eigenvalue, the molar mass and molar volume.

Affiliation: Chemistry Department, Faculty of Health and Medical Sciences, University of Surrey, Guildford, Surrey, United Kingdom.

ABSTRACTThe technique of Quantitative Structure Property Relationships has been applied to the glass transition temperatures of polyarylethersulphones. A general equation is reported that calculates the glass transition temperatures with acceptable accuracy (correlation coefficients of between 90-67%, indicating an error of 10-30% with regard to experimentally determined values) for a series of 42 reported polyarylethersulphones. This method is quite simple in assumption and relies on a relatively small number of parameters associated with the structural unit of the polymer: the number of rotatable bonds, the dipole moment, the heat of formation, the HOMO eigenvalue, the molar mass and molar volume. For smaller subsets of the main group (based on families of derivatives containing different substituents) the model can be simplified further to an equation that uses the volume of the substituents as the principal variable.

Mentions:
The greatest problems with the dataset were associated with estimating the flexibility of the chain, the parameter representing the degrees of freedom and the volume of the chain. The methods used were quite simplistic and insufficient to tackle the wider range of SRUs. Consequently, a smaller set of compounds was derived from the full dataset in order to find a correlation between the flexibility and Tg (Table 3) and between the volumes of substituents and Tg. Five base repeat units were identified (SRU ID 5, 10, 12, 22, 26) and their derivatives with various substituents were examined in more detail. The introduction of a stiffening group into the backbone is known to raise Tg and the data in Table 3 demonstrate how Tg is enhanced by the incorporation of more rigid bridges having lower rotational freedom or the potential for dipole-dipole interactions between adjacent polymer chains. An attempt was made to discern any relationships between the various calculated parameters and the magnitude of Tg. Figure 1 shows the scatter chart for the values of Tgversus dipole moment for the smaller subset of sulphone derivatives identified above. It is clear that no discernible relationship was evident, and this was the case for all of the parameters, save the volume of the substituent (Vsub), which is displayed in Figure 2. In this case, although there is some scatter evident at lower values of substituent volume, there does appear to be a trend of increasing Tg with increasing volume. Polyarylethersulphones in common with many synthetic polymers contain areas of amorphous chains and areas of crystallinity, the relative proportion of these regions can differ with the material and its method of preparation. This in turn would affect the glass transition values determined for the materials. Hence there is expected to be a scatter in the degree of correlation of the materials chosen and we have chosen to concentrate on those that give the best correlations. On this basis a series of graphs (Figures 3, 4, 5, 6, 7) were plotted for Vsubversus Tg for each of the individual derivatives. In addition to the original dataset, a series of 9 poly(arylether sulphone)s (originally published in reference 10), were also incorporated into the later plots and regressions. Three examples of polysulphones (based on the commercial polymer Victrex™) were included in the original data set and the parameters are presented in Table 4. Figure 3 depicts the relationship for Victrex™ PES (repeat unit 5) from which it can be seen that there is a linear correlation for Tg with increasing Vsub, albeit with a very small data set (n = 3), which is to be expected for only 3 examples. The SRU ID 22 is better represented in the data set and six examples are included in Table 5. Figure 4 depicts a clear and strong linear relationship for Tg with increasing Vsub, emphasising the utility of this approach. Unfortunately, although there is more information (with 7 data points) for the commercial polymer Radel™ R (ID 26) and its derivatives (Table 6), the plot of Tg and Vsub for (Figure 5), provides a less convincing relationship. There is an increasing trend discerned, but with large scatter in the data. The third commercial polymer (Udel™, ID 12) has the largest single data set (comprising 11 datapoints) (Table 7). This data set is the most disappointing and least convincing: the plot of Tg and Vsub for (Figure 6) shows no discernible relationship.

Mentions:
The greatest problems with the dataset were associated with estimating the flexibility of the chain, the parameter representing the degrees of freedom and the volume of the chain. The methods used were quite simplistic and insufficient to tackle the wider range of SRUs. Consequently, a smaller set of compounds was derived from the full dataset in order to find a correlation between the flexibility and Tg (Table 3) and between the volumes of substituents and Tg. Five base repeat units were identified (SRU ID 5, 10, 12, 22, 26) and their derivatives with various substituents were examined in more detail. The introduction of a stiffening group into the backbone is known to raise Tg and the data in Table 3 demonstrate how Tg is enhanced by the incorporation of more rigid bridges having lower rotational freedom or the potential for dipole-dipole interactions between adjacent polymer chains. An attempt was made to discern any relationships between the various calculated parameters and the magnitude of Tg. Figure 1 shows the scatter chart for the values of Tgversus dipole moment for the smaller subset of sulphone derivatives identified above. It is clear that no discernible relationship was evident, and this was the case for all of the parameters, save the volume of the substituent (Vsub), which is displayed in Figure 2. In this case, although there is some scatter evident at lower values of substituent volume, there does appear to be a trend of increasing Tg with increasing volume. Polyarylethersulphones in common with many synthetic polymers contain areas of amorphous chains and areas of crystallinity, the relative proportion of these regions can differ with the material and its method of preparation. This in turn would affect the glass transition values determined for the materials. Hence there is expected to be a scatter in the degree of correlation of the materials chosen and we have chosen to concentrate on those that give the best correlations. On this basis a series of graphs (Figures 3, 4, 5, 6, 7) were plotted for Vsubversus Tg for each of the individual derivatives. In addition to the original dataset, a series of 9 poly(arylether sulphone)s (originally published in reference 10), were also incorporated into the later plots and regressions. Three examples of polysulphones (based on the commercial polymer Victrex™) were included in the original data set and the parameters are presented in Table 4. Figure 3 depicts the relationship for Victrex™ PES (repeat unit 5) from which it can be seen that there is a linear correlation for Tg with increasing Vsub, albeit with a very small data set (n = 3), which is to be expected for only 3 examples. The SRU ID 22 is better represented in the data set and six examples are included in Table 5. Figure 4 depicts a clear and strong linear relationship for Tg with increasing Vsub, emphasising the utility of this approach. Unfortunately, although there is more information (with 7 data points) for the commercial polymer Radel™ R (ID 26) and its derivatives (Table 6), the plot of Tg and Vsub for (Figure 5), provides a less convincing relationship. There is an increasing trend discerned, but with large scatter in the data. The third commercial polymer (Udel™, ID 12) has the largest single data set (comprising 11 datapoints) (Table 7). This data set is the most disappointing and least convincing: the plot of Tg and Vsub for (Figure 6) shows no discernible relationship.

Bottom Line:
The technique of Quantitative Structure Property Relationships has been applied to the glass transition temperatures of polyarylethersulphones.A general equation is reported that calculates the glass transition temperatures with acceptable accuracy (correlation coefficients of between 90-67%, indicating an error of 10-30% with regard to experimentally determined values) for a series of 42 reported polyarylethersulphones.This method is quite simple in assumption and relies on a relatively small number of parameters associated with the structural unit of the polymer: the number of rotatable bonds, the dipole moment, the heat of formation, the HOMO eigenvalue, the molar mass and molar volume.

Affiliation:
Chemistry Department, Faculty of Health and Medical Sciences, University of Surrey, Guildford, Surrey, United Kingdom.

ABSTRACTThe technique of Quantitative Structure Property Relationships has been applied to the glass transition temperatures of polyarylethersulphones. A general equation is reported that calculates the glass transition temperatures with acceptable accuracy (correlation coefficients of between 90-67%, indicating an error of 10-30% with regard to experimentally determined values) for a series of 42 reported polyarylethersulphones. This method is quite simple in assumption and relies on a relatively small number of parameters associated with the structural unit of the polymer: the number of rotatable bonds, the dipole moment, the heat of formation, the HOMO eigenvalue, the molar mass and molar volume. For smaller subsets of the main group (based on families of derivatives containing different substituents) the model can be simplified further to an equation that uses the volume of the substituents as the principal variable.